Researchers from Harvard University and the Massachusetts Institute of Technology have demonstrated a surprising form of collective motion where pairs of atoms can move even when individual atoms are held immobile. The team realized a dipole-conserving Bose-Hubbard model using ultracold bosonic atoms in an optical lattice, effectively constraining particle movement while allowing pairs to move cooperatively and preserve the system’s overall dipole moment.
This work provides a bottom-up investigation of a Hamiltonian with kinetic constraints and allows for the exploration of low-energy phases of fractonic matter. In many-body systems, limiting the mobility of individual particles can fundamentally alter the nature of collective dynamics.
Dipole-Conserving Bose-Hubbard Model Enables Constrained Atomic Motion
Localized excitations consisting of a hole and a doublon were generated within a one-dimensional chain of ultracold bosonic atoms, enabling the observation of constrained quantum dynamics. The research team used site-resolved optical potentials to create these excitations and subsequently characterize their quantum walks and scattering dynamics, revealing strongly-correlated multi-particle behavior.
A strong linear potential effectively suppresses single-particle motion, leading to the conservation of the dipole moment, a phenomenon known as Wannier-Stark localization, yet interactions still allow for many-body dynamics. The system’s center of mass is identical to the dipole moment of the particle distribution, providing a simpler setting for studying these constrained interactions.
This process is akin to particle tunneling described by a Bose-Hubbard model, but with the added constraint of dipole conservation. The experimental platform allows for the exploration of ground-state phases predicted by the dipole-conserving Bose-Hubbard model, governed by the ratio of the coupling parameter J to the potential gradient Δ. Increasing J/Δ is expected to reveal rich phases such as fractured Bose droplets and dipole Luttinger liquids at higher fillings, and the expansion dynamics of localized excitations should provide a sensitive probe of these underlying phases.
Scattering experiments demonstrated strongly-interacting nature of dipole excitations, with suppressed nearest-neighbor and enhanced next-nearest-neighbor configurations providing clear evidence of strong nearest-neighbor interactions. The work realizes a kinetically constrained quantum system governed by a dipole-conserving Bose-Hubbard Hamiltonian, where single-particle motion is suppressed by a strong potential gradient and dipole moment conservation emerges as an effective symmetry.
The platform’s ability to initialize localized hole-doublon and doublon-hole excitations provides a unique tool for studying these interactions, and the observed scattering dynamics offer insights into the underlying many-body physics. The study’s findings suggest that collective motion can emerge even in systems where individual particle movement is restricted by strong external forces, challenging the expectation that such forces always lead to frozen dynamics. The ability to control and characterize these constrained dynamics opens up new avenues for exploring exotic quantum phases and understanding the interplay between interactions and localization in many-body systems.
Localized Hole-Doublon Pairs as Mobile Dipole Excitations
Localized hole-doublon pairs, created and observed in a chain of ultracold rubidium atoms, exhibit behavior suggesting they function as mobile dipole excitations, a phenomenon previously predicted but not directly observed. Researchers generated these excitations, consisting of a missing atom (hole) paired with a site containing two atoms (doublon), using site-resolved optical potentials applied to a one-dimensional lattice.
This precise control allowed for characterization of the excitations’ quantum walks and scattering dynamics, revealing insights into constrained quantum systems. The experimental setup uses a unique ability to isolate a single chain of atoms from a two-dimensional Mott insulator, a state of matter where each site holds exactly one atom.
Subsequent analysis, projecting the many-body state onto the Fock basis, revealed the coherent propagation of the dipole, confirming its stability as a quasiparticle within the dipole-Mott insulator regime. This contrasts with predictions for a dipole Luttinger liquid, where such excitations would produce asymmetric density profiles and diffusive waves. The ability to create and study these localized excitations offers a pathway to probe fractonic phases of matter, states where the fundamental excitations are immobile individually but can move collectively.
The energy spectrum of a two-particle, two-site system, as a function of the applied potential, showed how a dipole configuration (0, 2) can be created from an initial state (1, 1) by adiabatically ramping the potential. This controlled creation and manipulation of dipole excitations allows for detailed investigation of the underlying physics governing these exotic phases.
Strong Tilting Creates Wannier-Stark Localization & Fractons
This constraint, known as Wannier-Stark localization, suppresses individual particle movement while paradoxically allowing for many-body dynamics through correlated hopping processes that preserve the overall dipole moment. These processes create a scenario where interactions, rather than individual particle energies, govern the system’s behavior, a departure from traditional understandings of particle motion in lattices. The emergence of collective motion despite individual immobility stems from second-order tunneling processes, which maintain the total dipole moment throughout the system.
Visualizing this, a dipole, represented as an arrow between adjacent sites, indicates the direction of the dipole moment, highlighting how energy conservation and dipole moment preservation intertwine to dictate dynamics. This constrained behavior belongs to a broader class of fracton models, characterized by the conservation of multipole moments of a global charge, in this instance, the dipole moment associated with particle number.
Fractons, initially explored in the context of glassy spin dynamics and elasticity theory, are now gaining attention for their potential in understanding out-of-equilibrium many-body dynamics, including phenomena like Stark many-body localization and anomalous particle diffusion. Multipole moment conservation frequently leads to Hilbert space fragmentation, confining dynamics to numerous disconnected sectors beyond standard symmetry constraints. Recent experiments using tilted one- and two-dimensional optical lattices have revealed this fragmentation and the resulting non-ergodicity, as well as the presence of fractonic excitations.
However, until recently, direct experimental observation of individual bound states formed by these fractonic excitations remained elusive. Researchers have now generated and characterized these mobile bound states using ultracold atoms within a strongly tilted Bose-Hubbard chain, using the single-site resolution of a quantum gas microscope to prepare a localized hole-doublon pair, a “dipole excitation”, and track its evolution using full-counting statistics.
Given that energy conservation leads to strong nearest-neighbor interactions between these hole-doublon pairs, the dipole-conserving Hamiltonian imposes specific constraints at unity filling. Analysis of configurations reveals that, at intermediate times, nearest-neighbor configurations of the dipole pair are suppressed compared to the dynamics of on-site-Hubbard constraint bosons with the same tunneling amplitude. Instead, experimental and numerical results demonstrate that the dipole pair’s dynamics more closely resemble those of bosons with a nearest-neighbor-Hubbard constraint.
This suppression of nearest-neighbor configurations, coupled with an enhancement in next-nearest-neighbor configurations, indicates that the scattering dynamics of the dipole pair are governed by their strong nearest-neighbor interaction, effectively approaching the nearest-neighbor-Hubbard constraint limit. Similarly, a dipole-antidipole pair also exhibits a strong nearest-neighbor interaction.
The formation of a trion excitation of atoms is required for a dipole on the left nearest-neighbor link of an antidipole, resulting in an energy penalty imposed by the dipole-conserving Hamiltonian on these nearest-neighbor-dipole-antidipole configurations. Confirming the consistent role of nearest-neighbor interactions in shaping the behavior of these constrained excitations and providing a pathway to explore low-energy phases of fractonic matter.
Quantum Walks Characterized via Full-Counting Statistics
Characterizing the quantum walks of these excitations relies on full-counting statistics obtained through fluorescence imaging, a technique that allows researchers to precisely track the state of each atom in the optical lattice. This method isn’t simply about observing movement, but about quantifying the probability of finding the dipole excitations in specific configurations, and postselection of images based on both particle number and dipole moment minimizes the impact of imperfections in the initial atomic arrangement and preparation of the dipole.
This rigorous approach ensures the observed dynamics accurately reflect the underlying physics of the constrained system. The observed scattering dynamics of dipole pairs reveal a surprising suppression of nearest-neighbor configurations, diverging from the behavior expected of simple on-site or nearest-neighbor hardcore bosons.
Analysis of the experimental data, compared to exact diagonalization simulations demonstrates that dipole excitations behave more like particles that cannot occupy adjacent lattice sites, a characteristic known as hardcore behavior. The researchers found that the dynamics of a dipole-antidipole pair also exhibit strong nearest-neighbor interactions, further solidifying the importance of these constraints. Specifically, the team initialized both dipole-dipole and dipole-antidipole pairs with a four-link spacing and monitored their correlated quantum walks, comparing the results with simulations.
These experiments reveal that the dipole excitations exhibit ballistic expansion, with the two dipoles beginning to overlap at later times, allowing for the probing of their interactions through pair correlations extracted from the full-counting statistics. The ability to generate and characterize these mobile bound states, consisting of a localized hole and doublon, represents a step towards exploring low-energy phases of fractonic matter.
The study’s findings demonstrate that even with limited individual particle mobility, collective motion can still arise through subtle many-body effects. Byungmin Kang, Massachusetts Institute of Technology, and colleagues observed that the observed dynamics align closely with theoretical predictions based on the dipole-conserving Hubbard model, confirming the accuracy of their experimental approach. The detailed characterization of these quantum walks, using full-counting statistics, provides a powerful tool for understanding the emergent behavior of interacting particles in optical lattices.
Experimental Platform Probes Fractonic Phases of Matter
This observation moves beyond theoretical predictions by visualizing the behavior of these paired particles, known as hole-doublon pairs, as they interact and move within the lattice. The team’s approach centers on a dipole-conserving Bose-Hubbard model, where the overall dipole moment of the atomic distribution remains constant during movement. This constraint is imposed by suppressing single-site particle motion with a strong potential gradient, effectively freezing individual atoms but allowing pairs to move cooperatively.
Subsequent tracking of these excitations used full-counting statistics, a technique that provides detailed information about the quantum state of the system. These findings align with theoretical expectations for constrained-boson dynamics in one-dimensional lattices, where various low-energy phases, including dipole superfluids and supersolids, are predicted.
The experimental setup allowed for precise control over the system, starting with a unity-filled two-dimensional Mott insulator and isolating a single chain for observation. Initial lattice depths were carefully adjusted to freeze many-body dynamics before applying localized optical potentials to create the dipole excitations. This meticulous preparation and analysis were important for observing the subtle dynamics of the fractonic excitations.
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